-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1077993617813974955654021307368', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.9888308262251285, 0.14904226617617444], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.7330518718298263, 0.6801727377709194], 'a8': [0.0, 0.0], 'a9': [0.9555728057861407, -0.2947551744109042], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2934502274282054, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.9888308262251285, -0.14904226617617444]]], [7, [[1.0, 0], [0.7330518718298263, -0.6801727377709194]]]], 'bad_primes': [2, 3, 7], 'central_character': '588.305', 'coefficient_field': 'CDF', 'conductor': 588, 'conductor_radical': 42, 'conjugate': '2298421850495695692353508658053', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.9888308262251285, -0.14904226617617444]], [[1.0, 0], [0, 0], [0.7330518718298263, 0.6801727377709194]], [[1.0, 0], [0.7330518718298263, -0.6801727377709194]], [[1.0, 0], [0, 0], [-0.8262387743159949, -0.5633200580636221]], [[1.0, 0], [-0.4400711179528193, -1.9280775458253845], [-0.9009688679024191, 0.4338837391175581]], [[1.0, 0], [0, 0], [-0.36534102436639504, 0.9308737486442042]], [[1.0, 0], [-0.7330518718298263, -1.2696830865927278], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.36534102436639504, -0.9308737486442042]], [[1.0, 0], [0, 0], [-0.6234898018587335, -0.7818314824680298]], [[1.0, 0], [0.07473009358642425, -0.12943631894606392], [-0.5, -0.8660254037844386]], [[1.0, 0], [-0.12348980185873352, -1.6478568862524685], [-0.9888308262251285, 0.14904226617617444]], [[1.0, 0], [0, 0], [0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [-1.19157979868239, 1.4941938067078262], [-0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [0, 0], [-0.07473009358642425, 0.9972037971811801]], [[1.0, 0], [0, 0], [0.9888308262251285, 0.14904226617617444]], [[1.0, 0], [0, 0], [0.7330518718298263, -0.6801727377709194]], [[1.0, 0], [0.134658975633605, 1.7968991524286428], [-0.9888308262251285, 0.14904226617617444]], [[1.0, 0], [0.36534102436639504, -0.6327892162918554], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.6234898018587335, 0.7818314824680298]], [[1.0, 0], [1.211351760181443, 1.123970178357998], [0.07473009358642425, 0.9972037971811801]], [[1.0, 0], [0.07473009358642425, 0.12943631894606392], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.9009688679024191, 0.4338837391175581]], [[1.0, 0], [0, 0], [-0.8262387743159949, 0.5633200580636221]], [[1.0, 0], [0.4450418679126288, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-0.9555728057861407, 0.2947551744109042]], [[1.0, 0], [-0.6982198954451578, 1.77903527964921], [-0.7330518718298263, -0.6801727377709194]], [[1.0, 0], [0, 0], [-0.8262387743159949, 0.5633200580636221]], [[1.0, 0], [-0.6982198954451578, -0.21537231471315033], [0.8262387743159949, 0.5633200580636221]], [[1.0, 0], [0, 0], [0.9009688679024191, 0.4338837391175581]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-588-147.11-c0-0-0', 'leading_term': '0.60399697680846309755774607473039', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/588/1/z/a/305/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.6039969768084631, 0.5778500724404669, 0.5571945699731377, 0.5398878405733176, 0.5235137070718648, 0.5055937013479342, 0.4837444757609319, 0.45577089460752485, 0.4197082892928459, 0.37383463580462895, 0.31667018701866084, 0.24697569271841324, 0.16375473817822792, 0.06626200219354467, -0.0459828733971968, -0.1731771523545015, -0.3152143958147717, -0.4716632859791363, -0.6417477663534416, -0.8243302921324761, -1.0178998614271701, -1.2205663548935193, -1.430062548667035, -1.643754979846041, -1.8586646307814885, -2.0714981546608295, -2.2786900885430943, -2.476456191404304, -2.6608577064030556, -2.827875983238964, -2.9734965150953245, -3.0938010542140617, -3.1850660814543805, -3.243865530588088, -3.2671753211249004, -3.25247694844581, -3.1978571315343247, -3.1021003409487196, -2.9647709363310795, -2.7862816456842885, -2.567945227749136, -2.3120063812503058, -2.02165130443525, -1.7009927652918595, -1.3550291129765892, -0.9895763356845383, -0.6111730361586292, -0.22695903533442904, 0.15547079512646, 0.5282349558746876, 0.8833525735063217, 1.2129451882662914, 1.5094479798561784, 1.7658246427926803, 1.9757795710211157, 2.13396063244652, 2.2361456359855296, 2.2794056399440676, 2.262238537894641, 2.184666896051412, 2.0482948050376697, 1.8563195400497838, 1.6134950779160873, 1.3260459684972616, 1.0015316625092303, 0.6486631102589918, 0.2770752100433431, -0.1029395613085297, -0.4807293269340175, -0.845604258766025, -1.1871714431192204, -1.495672274980634, -1.762310798025562, -1.9795611021071664, -2.1414420126114604, -2.243747880562826, -2.284225316226065, -2.2626871917178013, -2.1810571404501395, -2.043340054629234, -1.8555166595877592, -1.6253630414827553, -1.3621989241469272, -1.0765714213260817, -0.779883814072827, -0.4839814982941547, -0.20070949460495094, 0.05854230116252775, 0.28328872388470644, 0.46437581899442515, 0.594366340254939, 0.6678672770014065, 0.6817840363057606, 0.6354882394674373, 0.5308890872526861, 0.37240181332078715, 0.16681075905631715, -0.07697108234985739, -0.3482397589798684, -0.6349246052681503, -0.9240842100937542, -1.20245557645728, -1.4570348652675287, -1.6756658336127501, -1.8476107309974188, -1.9640781126354387, -2.0186828332495086, -2.0078154177621164, -1.9309010366011643, -1.790532361433607, -1.5924655097111082, -1.3454739238438984, -1.0610611518489652, -0.7530398460403602, -0.43699059625668674, -0.12962017395151307, 0.15195590591078556, 0.3909771710574997, 0.571815714059513, 0.6807329132228807, 0.7065803932295307, 0.6414114348052843, 0.4809718168792818, 0.2250433954293398, -0.12238054503897065, -0.5531021975672302, -1.0549145663913264, -1.6119829442907991, -2.205401578099711, -2.8139060804198683, -3.4147142561284984, -3.9844611204280405, -4.500188360301337, -4.940344651761822, -5.285751340735295, -5.520488190900723, -5.632656266149279, -5.614979513319186, -5.465213100637754, -5.186334802783493, -4.786505362379133, -4.278794374749457, -3.6806793476958495, -3.0133366478809225, -2.300753509842683, -1.5686996123408006, -0.843604417405006, -0.1513920831612005, 0.48367104433774977, 1.0400608173257524, 1.4999582330837409, 1.8500425806457297, 2.0820739414904876, 2.1932339588386416, 2.186205358124243, 2.0689835297108625, 1.8544269439253387, 1.55956657514268, 1.2047071647763947, 0.8123643698087786, 0.4060909966815432, 0.009252073796858006, -0.3561879435873837, -0.6708022783463433, -0.9187027963257931, -1.0883507759630386, -1.1731328449332785, -1.1716694488262895, -1.0878372147340767, -0.9305018494511955, -0.7129739613637218, -0.4522155622890427, -0.1678391334703838, 0.11904678299012748, 0.38708219909736263, 0.6159212813152473, 0.7874475277479068, 0.8868689015822195, 0.903629054903722, 0.8320802643279966, 0.6718764671893962, 0.4280601822928173, 0.11083430255533329, -0.26497218742164064, -0.6807176083233016, -1.1149964266192969, -1.5448653512753192, -1.9471770736538432, -2.299944442778544, -2.5836546406007326, -2.782454356549332, -2.8851330864863005, -2.8858422517969746, -2.7845023342778625, -2.586867889877846, -2.3042401688612246, -1.952838004338517, -1.5528584137431385, -1.127277742923529, -0.7004609739159486, -0.2966599418078485, 0.06151021910252315, 0.3545236873658253, 0.5672350404282949, 0.689925893293803, 0.7190370458020822, 0.6575335418782182, 0.5148711222614757, 0.3065560759818086, 0.053315099162662534, -0.22008401616180387, -0.4862977002462927, -0.7170757115456268, -0.8850372857396198, -0.9654485920146966, -0.9378929939725358, -0.7877293970259828, -0.5072442328654747, -0.09641891708877284, 0.4367439314389306, 1.0763667913719808, 1.7993194003318203, 2.5762913213670076, 3.37326155861814, 4.15328660029574, 4.878507251780948, 5.512259248526654, 6.021163980909478, 6.377074401688063, 6.558757556392448, 6.5532089420998, 6.356514357673459, 5.974200921671128, 5.4210489933923265, 4.720369043008093, 3.9027801050734285, 3.004557285399549, 2.0656429141919816, 1.1274375852542133, 0.23050204204877514, -0.5876923707201426, -1.2948287262075038, -1.8654993258466823, -2.2825429079476587, -2.537882100231883, -2.6328096407274613, -2.577706122199973, -2.3912076510157894, -2.098876580231535, -1.731460128061683, -1.32284814448449, -0.9078607662834076, -0.5200078598067067, -0.1893641725524885, 0.05930323024897455, 0.20803499485784888, 0.24671104988709006], 'positive_zeros': ['0.850387021171205720859953640240042', '2.97447454796092782650989884802476', '4.17060743136478883305388648156974', '5.42272541426778125314327821033602', '6.04364205242385466211708240670800', '7.21533881119041739788078534254120', '7.72971333118621795649014534876252', '9.201820897671545335986412149331337', '10.06400492228243681979513855960726', '10.78633089672602809975906214179508'], 'prelabel': '2-588-147.11-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5417104645732861, 'root_angle': -0.3945578231292517, 'root_number': '0.32523134988754714627901667587550 - 0.94563447962218672837451281764749*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.19727891156462585', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.850387021171205720859953640240', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.97447454796092782650989884802', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.17060743136478883305388648157', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.2934502274282054, 'bad_primes': [2, 3, 7], 'central_character': '147.11', 'conductor': 588, 'conductor_radical': 42, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/588/1/z/a/305/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-588-147.11-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-588-147.11-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5417104645732861, 'root_angle': -0.19727891156462585, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.850387021171205720859953640240', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1077993617813974955654021307368', 'Lhash_array': ['1077993617813974955654021307368'], 'label': '2-588-147.11-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/588/1/z/a/305/1'}